Full-DoF Egomotion Estimation for Event Cameras Using Geometric Solvers

TL;DR

This work addresses the challenge of recovering full-DoF egomotion for event cameras without auxiliary sensors. It introduces two sparse geometric solvers based on line-incidence geometry and coplanarity of normals to jointly estimate angular and linear velocities under a locally constant-velocity model, using an Adam-based optimization framework with first-order rotation approximations for fast initialization. The methods are validated through synthetic experiments and real-world data, demonstrating accurate velocity estimation and robust performance under noise and line geometry variations, with explicit handling of pure-rotation cases. The results enable more capable event-camera VIO/SLAM integration by providing reliable, sensor-free full-DoF motion estimates from asynchronous event streams.

Abstract

For event cameras, current sparse geometric solvers for egomotion estimation assume that the rotational displacements are known, such as those provided by an IMU. Thus, they can only recover the translational motion parameters. Recovering full-DoF motion parameters using a sparse geometric solver is a more challenging task, and has not yet been investigated. In this paper, we propose several solvers to estimate both rotational and translational velocities within a unified framework. Our method leverages event manifolds induced by line segments. The problem formulations are based on either an incidence relation for lines or a novel coplanarity relation for normal vectors. We demonstrate the possibility of recovering full-DoF egomotion parameters for both angular and linear velocities without requiring extra sensor measurements or motion priors. To achieve efficient optimization, we exploit the Adam framework with a first-order approximation of rotations for quick initialization. Experiments on both synthetic and real-world data demonstrate the effectiveness of our method. The code is available at https://github.com/jizhaox/relpose-event.

Figures (5)

• Figure 1: Incidence relation between the observed line $\mathbf{L}$ and line $\mathbf{L}^e_j$ of the $j$-th event. The line $\mathbf{L}^e_j$ is consistent with the bearing vector $\mathbf{f}'_j$. The vector $\hat{\mathbf{v}}$ represents the projection of the translation $\mathbf{v}$ onto the plane spanned by the vectors $\mathbf{e}_2^\ell$ and $\mathbf{e}_3^\ell$, which is filled by dot patterns. Due to the aperture problem, only $u^\ell_y$ and $u^\ell_z$ components are observable.
• Figure 2: Coplanarity relation between plane normal vectors. Plane normal $\mathbf{n}_j$ can be computed from the event $e_j$ and its normal flow $\mathbf{g}_j$. The line direction vector $\mathbf{h}_j$ in the image plane is perpendicular with $\mathbf{g}_j$ within the image plane. The line $\mathbf{L}$ is orthogonal to the plane normal set $\{\mathbf{n}'_j\}_{j=1}^N$.
• Figure 3: The results on synthetic data demonstrate the relationship between errors and various factors, such as the number of events, number of lines, and noise levels.
• Figure 4: Landscape of the objective functions $\lambda_{\text{min}}$. The events for each line is set as $N = 100$. For better visualization, the pseudocolor and colormap of the objectives use the logarithmic scale.
• Figure 5: Line cluster extraction from the desk-normal sequence in the VECtor dataset. (a) An event frame generated by accumulating events, where red and blue dots represent events with opposite polarities. (b) The corresponding image. (c) Results of line segment detection. (d) Line cluster extraction by associating events near the line segments. If an event is within $5$ pixels of a line segment, draw a circle at the event's position.

Theorems & Definitions (4)

• Proposition 1
• proof
• Proposition 2
• proof